4x-36=36+1/3x

Solution for 4x-36=36+1/3x equation:

4x-36=36+1/3x

We move all terms to the left:

4x-36-(36+1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(1/3x+36)-36=0

We get rid of parentheses

4x-1/3x-36-36=0

We multiply all the terms by the denominator


4x*3x-36*3x-36*3x-1=0

Wy multiply elements

12x^2-108x-108x-1=0

We add all the numbers together, and all the variables

12x^2-216x-1=0

a = 12; b = -216; c = -1;
Δ = b2-4ac
Δ = -2162-4·12·(-1)
Δ = 46704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{46704}=\sqrt{16*2919}=\sqrt{16}*\sqrt{2919}=4\sqrt{2919}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-4\sqrt{2919}}{2*12}=\frac{216-4\sqrt{2919}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+4\sqrt{2919}}{2*12}=\frac{216+4\sqrt{2919}}{24}
$